In order to measure the color of a light emitting object (e.g., a light emitting diode (LED) lamp, a computer monitor, a television, a projector, or the like), a color measuring instrument such as a colorimeter should be able to output color measurement values that correspond to the color matching functions (CMFs) of the standard observer (according to Commission internationale de l'éclairage (CIE 1931)).
It is very difficult, however, to design a color measurement instrument whose three sensors match the CMFs exactly. Typically, a mathematical transformation is used to transform measurements made by the sensors to CMF-matching values.